Question

Suppose relation R(A,B) has the tuples:

A B
1 2
3 4
5 6

and the relation S(B,C,D) has tuples:
B C D
2 4 6
4 6 8
4 7 9


Compute the theta-join of R and S with the condition R.A < S.C ANDR.B < SD. Then, identify from the list below one of the tuples in R 1×R·A < S.C AND R.Ba) (3,4,4,6,8)
b) (3,4,5,7,9)
c) (1,2,4,4,6)
d) (1,2,2,6,8)

Answer 1

The theta-join of R and S with the conditions R.A < S.C AND R.B < S.D results in tuples (3,4,4,6,8), (3,4,4,7,9), and (1,2,4,6,8). One of the correct tuples from the given options is (3,4,4,6,8).

Step-by-step explanation:

The theta-join of R and S based on the condition R.A < S.C AND R.B < S.D requires us to look at tuples in relation R and S and compare the values as per the given conditions. For each tuple in R, we check if there is a tuple in S such that the condition holds true. If it does, we include the concatenated tuple in our result set.

Upon inspection of the provided tuples, we can determine that:

• The tuple (3,4) from R can join with (4,6,8) and (4,7,9) from S because 3 < 6 and 4 < 8, and also 3 < 7 and 4 < 9.
• The tuple (1,2) from R can join with (4,6,8) from S because 1 < 6 and 2 < 8.
• The tuple (5,6) from R cannot join with any tuple from S because there's no tuple in S where 5 < C.

After performing the theta-join, we get the following resulting tuples:

• (3,4,4,6,8)
• (3,4,4,7,9)
• (1,2,4,6,8)

Therefore, one of the tuples from the given list that is in the result of the theta-join is (3,4,4,6,8).